The evolution of continental ice sheets introduces a long time scale in the climate system. Large ice sheets have a memory of millenia, hence the present-day ice sheets of Greenland and Antarctica are still adjusting to climatic variations extending back to the last glacial period. This trend is separate from the direct response to mass-balance changes on decadal time scales and needs to be correctly accounted for when assessing current and future contributions to sea level. One way to obtain estimates of current ice mass changes is to model the past history of the ice sheets and their underlying beds over the glacial cycles. Such calculations assist to distinguish between the longer-term ice-dynamic evolution and short-term mass-balance changes when interpreting altimetry data, and are helpful to isolate the effects of postglacial rebound from gravity and altimetry trends. The presentation will discuss results obtained from 3-D thermomechanical ice-sheet/lithosphere/bedrock models applied to the Antarctic and Greenland ice sheets. The simulations are forced by time-dependent boundary conditions derived from sediment and ice core records and are constrained by geomorphological and glacial-geological data of past ice sheet and sea-level stands. Current simulations suggest that the Greenland ice sheet is close to balance, while the Antarctic ice sheet is still losing mass, mainly due to incomplete grounding-line retreat of the West Antarctic ice sheet since the LGM. The results indicate that altimetry trends are likely dominated by ice thickness changes but that the gravitational signal mainly reflects postglacial rebound.